Question: The geometric sequence $(a_i)$ is defined by the formula: $a_i = -\dfrac{5}{2} \left(2\right)^{i - 1}$ What is $a_{2}$, the second term in the sequence?
Solution: From the given formula, we can see that the first term of the sequence is $-\dfrac{5}{2}$ and the common ratio is $2$ The second term is simply the first term times the common ratio. Therefore, the second term is equal to $a_2 = -\dfrac{5}{2} \cdot 2 = -5$.